A147983 A sequence from a 3 X n Chomp game, see the first comment.

120, 400, 402, 422, 424, 513, 576, 583, 585, 593, 605, 610, 861, 888, 890, 892, 904, 1013, 1015, 1059, 1129, 1141, 1143, 1163, 1216, 1281, 1291, 1293, 1295, 1419, 1448, 1508, 15231525, 1537, 1561, 1723, 1747, 1824, 1868, 1870, 1875, 1889, 2003, 2010

Offset

1,1

Comments

Values of r where a P-position (p,q,r) has a pattern. This algorithm is very efficient. When the length of a period and the start matrix are not of interest (only whether r has or does not have a pattern), the algorithm generates the sequence: 120, 400, 402, ..., 10501, 10583, 10585 very quickly.

First step: generate all the P-positions, where, for example, n = 15000. Second step: run the algorithm.

From Petros Hadjicostas, Apr 11 2020: (Start)

From A. E. Brouwer's website (see below): "Chomp is a game played on a partially ordered set P with smallest element 0. A move consists of picking an element x of P and removing x and all larger elements from P. Whoever picks 0 loses."

"In 3-by-n Chomp, a game position is (p,q,r) with p not less than q and q not less than r.

If r = 0 then this is really 2-by-n Chomp, and the P-positions (previous player wins) are those with p = q+1.

If r = 1, the only P-positions are (3,1,1) and (2,2,1).

If r = 2, the P-positions are those with p = q+2.

If r = 3, the P-positions are (6,3,3), (7,4,3) and (5,5,3).

If r = 4, the P-positions are (8,4,4), (9,5,4), (10,6,4) and (7,7,4).

If r = 5, the P-positions are (10,5,5), (9,6,5) and (a+11,a+7,5) for nonnegative a." (For more details, see his web page.) (End)

Links

Table of n, a(n) for n=1..44.

Emily Bergman, Game theory and an explanation of a 3 x n Chomp! Boards, Senior Mathematics Project,  Lynchburg College, 2014. (See also here.)

Andries E. Brouwer, The game of Chomp.

Eva Elduque, The game of CHOMP, Madison Math Circle, Department of Mathematics, UW-Madison.

E. J. Friedman and A. S. Landsberg, Scaling, renormalization, and universality in combinatorial games: The geometry of Chomp, in: A. Dress, Y. Xu, and B. Zhu (eds), Combinatorial Optimization and Applications, COCOA 2007 (Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg).

David Gale, A curious Nim-type game, American Mathematical Monthly 81(8) (1974), 876-879.

T. Khandhawit and L. Ye, Chomp on graphs and subsets, arXiv:1101.2718 [math.CO], 2011.

Wikipedia, Chomp.

Doron Zeilberger, Three-rowed CHOMP, Advances in Applied Mathematics 26 (2001), 168-179.

Doron Zeilberger, Chomp, recurrences and Chaos(?), Journal of Difference Equations and Applications 10(13-15) (2004), 1281-1293.

Doron Zeilberger, All the winning bites for a by b Chomp for a and b up to 14 and two computational challenges, Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, 2018; Local copy, pdf file only, no active links

Crossrefs

Cf. A029899, A029900, A029901, A029902, A029903, A029904, A029905.

Sequence in context: A354624 A226884 A273509 * A307933 A235239 A337469

Adjacent sequences: A147980 A147981 A147982 * A147984 A147985 A147986

Keyword

nonn

Author

Csaba Beretka (bcs183(AT)freemail.hu), Nov 18 2008

Extensions

Name edited by Petros Hadjicostas, Apr 11 2020

Status

approved